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Geometric Perturbation Theory In Physics
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Book Synopsis Geometric Perturbation Theory in Physics by : Stephen Malvern Omohundro
Download or read book Geometric Perturbation Theory in Physics written by Stephen Malvern Omohundro and published by World Scientific. This book was released on 1986 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book which focusses on mechanics, waves and statistics, describes recent developments in the application of differential geometry, particularly symplectic geometry, to the foundations of broad areas of physics. Throughout the book, intuitive descriptions and diagrams are used to elucidate the mathematical theory. It develops a coordinate-free framework for perturbation theory and uses this to show how underlying symplectic structures arise from physical asymptotes. It describes a remarkable parity between classical mechanics which arises asymptotically from quantum mechanics and classical thermodynamics which arises asymptotically from statistical mechanics. Included here is a section with one hundred unanswered questions for further research.
Book Synopsis Geometric Perturbation Theory and Plasma Physics by :
Download or read book Geometric Perturbation Theory and Plasma Physics written by and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Book Synopsis Geometric Perturbation Theory and Plasma Physics by : Stephen Malvern Omohundro
Download or read book Geometric Perturbation Theory and Plasma Physics written by Stephen Malvern Omohundro and published by . This book was released on 1985 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Perturbation Methods by : Ali H. Nayfeh
Download or read book Perturbation Methods written by Ali H. Nayfeh and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research
Book Synopsis Differential Geometric Methods in Theoretical Physics by : Ling-Lie Chau
Download or read book Differential Geometric Methods in Theoretical Physics written by Ling-Lie Chau and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: After several decades of reduced contact, the interaction between physicists and mathematicians in the front-line research of both fields recently became deep and fruit ful again. Many of the leading specialists of both fields became involved in this devel opment. This process even led to the discovery of previously unsuspected connections between various subfields of physics and mathematics. In mathematics this concerns in particular knots von Neumann algebras, Kac-Moody algebras, integrable non-linear partial differential equations, and differential geometry in low dimensions, most im portantly in three and four dimensional spaces. In physics it concerns gravity, string theory, integrable classical and quantum field theories, solitons and the statistical me chanics of surfaces. New discoveries in these fields are made at a rapid pace. This conference brought together active researchers in these areas, reporting their results and discussing with other participants to further develop thoughts in future new directions. The conference was attended by SO participants from 15 nations. These proceedings document the program and the talks at the conference. This conference was preceded by a two-week summer school. Ten lecturers gave extended lectures on related topics. The proceedings of the school will also be published in the NATO-AS[ volume by Plenum. The Editors vii ACKNOWLEDGMENTS We would like to thank the many people who have made the conference a success. Furthermore, ·we appreciate the excellent talks. The active participation of everyone present made the conference lively and stimulating. All of this made our efforts worth while.
Book Synopsis From Classical Field Theory to Perturbative Quantum Field Theory by : Michael Dütsch
Download or read book From Classical Field Theory to Perturbative Quantum Field Theory written by Michael Dütsch and published by Springer. This book was released on 2019-03-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained. The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.
Book Synopsis Symmetry and Perturbation Theory by : Simonetta Abenda
Download or read book Symmetry and Perturbation Theory written by Simonetta Abenda and published by World Scientific. This book was released on 2002 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth conference on OC Supersymmetry and Perturbation TheoryOCO (SPT 2002). The proceedings present original results and state-of-the-art reviews on topics related to symmetry, integrability and perturbation theory, etc. Contents: An Outline of the Geometrical Theory of the Separation of Variables in the Hamilton-Jacobi and SchrAdinger Equations (S Benenti); Partial Symmetries and Symmetric Sets of Solutions to PDE's (G Cicogna); On the Algebro-Geometric Solution of 3 x 3 Matrix Riemann-Hilbert Problem (V Enolski & T Grava); Bifurcations in Flow-Induced Vibration (S Fatimah & F Verhulst); Steklov-Lyapunov Type Systems (Yu N Fedorov); Renormalization Group and Summation of Divergent Series for Hyperbolic Invariant Tori (G Gentile); On the Linearization of Holomorphic Vector Fields in the Siegel Domain with Linear Parts Having Nontrivial Jordan Blocks (T Gramchev); Smooth Normalization of a Vector Field Near an Invariant Manifold (A Kopanskii); Inverse Problems for SL (2) Lattices (V B Kuznetsov); Some Remarks about the Geometry of Hamiltonian Conservation Laws (J-P Ortega); Janet's Algorithm (W Plesken); Some Integrable Billiards (E Previato); Symmetries of Relative Equilibria for Simple Mechanical Systems (M Rodr guez-Olmos & M E Sousa Dias); A Spectral Sequences Approach to Normal Forms (J A Sanders); Rational Parametrization of Strata in Orbit Spaces of Compact Linear Groups (G Sartori & G Valente); Effective Hamiltonians and Perturbation Theory for Quantum Bound States of Nuclear Motion in Molecules (V G Tyuterev); Generalized Hasimoto Transformation and Vector Sine-Gordon Equation (J P Wang); and other papers. Readership: Researchers and graduate students in mathematical and theoretical physics, and nonlinear science."
Book Synopsis Quantum Field Theory I: Basics in Mathematics and Physics by : Eberhard Zeidler
Download or read book Quantum Field Theory I: Basics in Mathematics and Physics written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2007-04-18 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
Book Synopsis Geometric And Algebraic Topological Methods In Quantum Mechanics by : Luigi Mangiarotti
Download or read book Geometric And Algebraic Topological Methods In Quantum Mechanics written by Luigi Mangiarotti and published by World Scientific. This book was released on 2005-01-27 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Book Synopsis Geometric Perturbation Theory and Plasma Physics by : Stephen Malvern Omohundro
Download or read book Geometric Perturbation Theory and Plasma Physics written by Stephen Malvern Omohundro and published by . This book was released on 1985 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to the Perturbation Theory of Hamiltonian Systems by : Dmitry Treschev
Download or read book Introduction to the Perturbation Theory of Hamiltonian Systems written by Dmitry Treschev and published by Springer. This book was released on 2010-04-29 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an extended version of lectures given by the ?rst author in 1995–1996 at the Department of Mechanics and Mathematics of Moscow State University. We believe that a major part of the book can be regarded as an additional material to the standard course of Hamiltonian mechanics. In comparison with the original Russian 1 version we have included new material, simpli?ed some proofs and corrected m- prints. Hamiltonian equations ?rst appeared in connection with problems of geometric optics and celestial mechanics. Later it became clear that these equations describe a large classof systemsin classical mechanics,physics,chemistry,and otherdomains. Hamiltonian systems and their discrete analogs play a basic role in such problems as rigid body dynamics, geodesics on Riemann surfaces, quasi-classic approximation in quantum mechanics, cosmological models, dynamics of particles in an accel- ator, billiards and other systems with elastic re?ections, many in?nite-dimensional models in mathematical physics, etc. In this book we study Hamiltonian systems assuming that they depend on some parameter (usually?), where for?= 0 the dynamics is in a sense simple (as a rule, integrable). Frequently such a parameter appears naturally. For example, in celestial mechanics it is accepted to take? equal to the ratio: the mass of Jupiter over the mass of the Sun. In other cases it is possible to introduce the small parameter ar- ?cially.
Book Synopsis Geometric Phases in Physics by : Frank Wilczek
Download or read book Geometric Phases in Physics written by Frank Wilczek and published by World Scientific. This book was released on 1989 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as ?Berry's phase?) in addition to the usual dynamical phase derived from Schrdinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified and found to be important in a startling variety of physical contexts, ranging from nuclear magnetic resonance and low-Reynolds number hydrodynamics to quantum field theory. This volume is a collection of original papers and reprints, with commentary, on the subject.
Book Synopsis Perturbation theory for linear operators by : Tosio Kato
Download or read book Perturbation theory for linear operators written by Tosio Kato and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Geometry of Manifolds with Symmetry by : V.V. Trofimov
Download or read book Introduction to Geometry of Manifolds with Symmetry written by V.V. Trofimov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: One ofthe most important features of the development of physical and mathematical sciences in the beginning of the 20th century was the demolition of prevailing views of the three-dimensional Euclidean space as the only possible mathematical description of real physical space. Apriorization of geometrical notions and identification of physical 3 space with its mathematical modellR were characteristic for these views. The discovery of non-Euclidean geometries led mathematicians to the understanding that Euclidean geometry is nothing more than one of many logically admissible geometrical systems. Relativity theory amended our understanding of the problem of space by amalgamating space and time into an integral four-dimensional manifold. One of the most important problems, lying at the crossroad of natural sciences and philosophy is the problem of the structure of the world as a whole. There are a lot of possibilities for the topology offour dimensional space-time, and at first sight a lot of possibilities arise in cosmology. In principle, not only can the global topology of the universe be complicated, but also smaller scale topological structures can be very nontrivial. One can imagine two "usual" spaces connected with a "throat", making the topology of the union complicated.
Book Synopsis The Physics of Phase Space by : Young S. Kim
Download or read book The Physics of Phase Space written by Young S. Kim and published by Springer. This book was released on 2005-09-13 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of phase space plays a decisive role in the study of the transition from classical to quantum physics. This is particularly the case in areas such as nonlinear dynamics and chaos, geometric quantization and the study of the various semi-classical theories, which are the setting of the present volume. Much of the content is devoted to the study of the Wigner distribution. This volume gives the first complete survey of the progress made by both mathematicians and physicists. It will serve as an excellent reference for further research.
Book Synopsis Quantum Physics and Geometry by : Edoardo Ballico
Download or read book Quantum Physics and Geometry written by Edoardo Ballico and published by Springer. This book was released on 2019-03-13 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.
Book Synopsis Geometry and Theoretical Physics by : Joachim Debrus
Download or read book Geometry and Theoretical Physics written by Joachim Debrus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interaction between geometry and theoretical physics has often been very fruitful. A highlight in this century was Einstein's creation of the theory of general relativity. Equally impressive was the recognition, starting from the work of Yang and Mills and culminating in the Weinberg-Salam theory of the electroweak interaction and quantum chromodynamics, that the fundamental interactions of elementary particles are governed by gauge fields, which in ma thematical terms are connections in principal fibre bundles. Theoretical physi cists became increasingly aware of the fact that the use of modern mathematical methods may be necessary in the treatment of problems of physical interest. Since some of these topics are covered at most summarily in the usual curricu lum, there is a need for extra-curricular efforts to provide an opportunity for learning these techniques and their physical applications. In this context we arranged a meeting at the Physikzentrum Bad Ronnef 12-16 February 1990 on the subject "Geometry and Theoretical Physics", in the series of physics schools organized by the German Physical Society. The participants were graduate students from German universities and research institutes. Since the meeting occurred only a short time after freedom of travel between East and West Germany became a reality, this was for many from the East the first opportunity to attend a scientific meeting in the West, and for many from the West the first chance to become personally acquainted with colleagues from the East.
